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Assertion (A): The origin does not lie in any quadrant. Reason (R): The quadrants are the four regions lying strictly off the axes, and the origin lies on both axes. Which is correct?

Class 9Coordinate GeometryCoordinate Geometry
  • AA is true but R is false
  • BA is false but R is true
  • CBoth A and R are false
  • DBoth A and R are true and R correctly explains A

Step-by-Step Solution

The origin (0, 0) lies on the -axis and on the -axis, and a point on an axis belongs to no quadrant. Both statements are true, and R gives exactly the reason for A.
Answer: D) Both A and R are true and R correctly explains A

Key idea: Special points

- **Origin**: (0, 0).
- **On -axis**: , so the form is (a, 0). Examples: (3, 0), (−5, 0).
- **On -axis**: , so the form is (0, b). Examples: (0, 7), (0, −2).
- **First-quadrant point**: both positive.
- **Third-quadrant point**: both negative.

Knowing which axis or quadrant a point belongs to is a quick check that you've plotted it correctly.

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